Unbounded asymptotic equivalences of operator nets with applications
Positivity, cilt.23, sa.4, ss.829-851, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 23 Sayı: 4
- Basım Tarihi: 2019
- Doi Numarası: 10.1007/s11117-018-0640-z
- Dergi Adı: Positivity
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.829-851
- Anahtar Kelimeler: Unbounded convergence, Asymptotic equivalence, Operator nets
- TED Üniversitesi Adresli: Hayır
Özet
Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and d on a vector lattice, we study d-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, paper focuses on d-martingale and d-Lotz–Räbiger nets.